This invention relates in general to a piezoelectric energy conversion apparatus and, in particular, to one with high energy conversion efficiency. More particularly, this invention relates to a piezoelectric transformer having modal-shaped electrode for efficiently converting electric power.
Piezoelectricity is widely utilized in various applications. As a transducer for converting energy in one form into another, a piezoelectric material block is useful as a workpiece for converting mechanical energy to electrical or vice versa. A piezoelectric workpiece can be used to convert an electrical power at one AC frequency and voltage into another at different frequency and voltage. This specific application of AC electrical power conversion involving converted (frequently raised) voltage makes a piezoelectric transducer device a useful piezoelectric transformer suitable for various industrial and consumer applications.
Charles A. Rosen proposed his piezoelectric transformer in the 1950""s. It is not until the 1990""s when piezoelectric transformer has become more and more popular in electronic devices. Piezoelectric transformers have been used such as in the power supply section of various electronic devices, portable ones in particular. Due to benefits such as their size and weight, it is obvious that piezoelectric transformers will become even more popular. Improved safety is another desirable feature of a piezoelectric transformer. A failed piezoelectric transformer normally breaks itself and ceases to function. Fire hazards are virtually of no concern at the part of the piezoelectric workpiece itself.
Electrodes plated to the surface of a piezoelectric material block are necessary for conveying electric power into and/or out of the workpiece in order for the piezoelectric system to function. Traditionally, dimensioning factors including both shape and size of the electrodes have not been carefully considered parameters when designing a piezoelectric system. Typically, rectangular-shaped electrodes are used for rectangular-shaped workpieces. In disk- or ring-shaped workpieces, electrodes are typically also disk-shaped or having the shape of a section of the disk or ring. These electrode shape configurations are considered uniform electrodes in the description of the present invention.
Traditionally, piezoelectric systems have been analyzed based on circuit theories. Mechanical considerations of a piezoelectric system are xe2x80x9ctranslatedxe2x80x9d into parameters that are fit into circuit models. Piezoelectric workpieces thus developed are not optimized in issues such as energy conversion efficiency and parasitic noisesxe2x80x94signals at undesirable frequencies with sufficiently significant amplitudes mixed in the output of a piezoelectric workpiece.
FIG. 1 is a perspective view of a piezoelectric workpiece outlining the definition of the piezoelectric parameters, both electrical and mechanical, and material orientation and dimensions for the analysis of a piezoelectric system. As is illustrated, the piezoelectric workpiece 100 is, in general, an elongated thin rectangular-shaped plate having a length L, a width W and a thickness, or height, H. Note that in the following theoretical development for the description of the piezoelectric transducer apparatus of the present invention, the IEEE Compact Matrix Notation system is employed.
By convention, the two largest surfaces of the elongated thin-plate workpiece are the side surfaces, and the two smallest are the end surfaces. The direction along the longitudinal axis of the workpiece is the first orientation, that perpendicular to the first orientation and parallel to the side surfaces is the second, and that perpendicular both to the side surfaces and to the longitudinal axis is the third, as is shown in the drawing by an orientation axis system 110 labeled with orientations 1, 2 and 3 respectively.
Also, in the theoretical development of the invention in the following detailed description, a variable x is set up along the direction of the first orientation. This coordinate axis, one measuring the longitudinal dimension, or length, of the elongated workpiece 100, serves as a variable in the analysis of the piezoelectric system according to the teaching of the present invention. One end of the workpiece 100 is set conveniently as the origin of the x coordinate axis, as is seen in FIG. 1.
The workpiece 100 has a side-plated electrode 102 and another not shown in the perspective view. That electrode which opposes electrode 102 and provides for a complete electrical circuit path is plated on the other side of the workpiece opposite to the side for the electrode 102.
Each of the electrodes is connected to a corresponding terminal of an electric circuit 120, represented in the drawing by a voltage sign V that signifies a voltage across the electrodes of the piezoelectric workpiece. The current corresponding to the voltage V in the circuit 120 is identified by I. P represents the electrical power arising from voltage V and current I.
External mechanical forces applied to the workpiece 100 is identified in the drawing by the symbol F, the corresponding mechanical velocity induced as a result of an applied force F is identified by U.
The piezoelectric system of FIG. 1, which has a workpiece 100 with side-plated electrodes including 102, is in the 31 mode, i.e., the polarization is in orientation 3, and the mechanical vibration is in orientation 1. By contrast, a system such as that illustrated in FIG. 3 which has a workpiece 300 with end-plated electrodes 302 and 304 is in 33 mode. Both its electrical polarization and mechanical vibration are along orientation 3 of its orientation axis system 310.
Based on the traditional method of analysis that relies on circuit theories, a piezoelectric system such as that depicted in FIG. 1 which has side-plated electrodes and operates in the 31 mode has the following constitutive equations:
S1=s11ET1+d31E3xe2x80x83xe2x80x83(1) 
D3=d31T1+xcex533TE3.xe2x80x83xe2x80x83(2) 
In Equations (1), (2) and those to be discussed below, the parameters and constants are in accordance with their respective definitions in the IEEE notation system mentioned above.
Based on the relationship between the piezoelectric constants and between the longitudinal strain u and the longitudinal stress S1, considering the longitudinal motion equation for the system, the following governing equation may be derived for the 31 mode piezoelectric workpiece:                                                         -              ρ                        ⁢                                                            ∂                  2                                ⁢                u                                            ∂                                  t                  2                                                              +                                    c              11              E                        ⁢                                                            ∂                  2                                ⁢                u                                            ∂                                  x                  2                                                                    =                              E            3                    ⁢                                                    ∂                                  e                  31                                                            ∂                x                                      .                                              (        3        )            
Since a conventional piezoelectric workpiece employs uniform electrodes characterized by its rectangular-shaped electrode patterns, Equation (3) may thus be reduced to:                                                         -              ρ                        ⁢                                                            ∂                  2                                ⁢                u                                            ∂                                  t                  2                                                              +                                    c              11              E                        ⁢                                                            ∂                  2                                ⁢                u                                            ∂                                  x                  2                                                                    =        0.                            (        4        )            
Equation (4) is a homogeneous one-dimensional wave equation, which has a general solution for the longitudinal strain u that can be expressed as
u=(B1 sin xcex2x+B2 cos xcex2x)ejxcfx89txe2x80x83xe2x80x83(5) 
wherein
xcex2=xcfx89/cxe2x80x83xe2x80x83(6) 
and
c={square root over (c11E/xcfx81)},xe2x80x83xe2x80x83(7) 
in which j={square root over (xe2x88x921)}, xcfx89 is the angular frequency, xcex2 is the wave number, c is the velocity of wave propagation, and B1 and B2 are, respectively, coefficients to be determined by the boundary condition of the examined system.
In addition to the mechanical piezoelectric parameters as incorporated into the analysis above, electrical ones also need to be considered in the analysis as well. In a 31 mode piezoelectric system of FIG. 1, the electromechanical coupling coefficient can be defined to be                               k          31          2                =                                                            d                31                2                            ⁢                              c                11                E                                                    ϵ              33              T                                .                                    (        8        )            
Assuming that the 31 mode piezoelectric workpiece in the system is clamped at its both ends, the mechanical characteristic impedance of the workpiece transmitting mechanical waves can be described as
Z0=HWxcfx81c=HW{square root over (xcfx81c11E)}.xe2x80x83xe2x80x83(9) 
In a traditional analysis approach based on circuit theories, mechanical parameters of force and velocity in a piezoelectric system are considered in an analogy and treated as the equivalents of another parameter pair of voltage and current respectively. Based on such an analogy, a 31 mode piezoelectric system can be shown to have an equivalent transformer step-up ratio of
N=Wd31c11E.xe2x80x83xe2x80x83(10) 
FIG. 2 shows the equivalent circuit of the 31 mode piezoelectric system of FIG. 1. The circuit configuration in this equivalent circuit is obtained utilizing the conventional technique of circuit analysis as described above. Characteristics of the equivalent circuit, namely, those of a 31 mode piezoelectric transformer as defined by the system of FIG. 1 are outlined in the drawing. These include the mechanical characteristic impedance Z0, the wave number xcex2, the velocity of wave propagation c, the electromechanical coupling coefficient k312, and the equivalent step-up ratio N.
Based on the same circuit theories, another piezoelectric system, one in the 33 mode as outlined in FIG. 3, may be shown to have an equivalent circuit illustrated in FIG. 4, which is derived from the following governing equation                                                         -              ρ                        ⁢                                                            ∂                  2                                ⁢                w                                            ∂                                  t                  2                                                              +                                    c              33              D                        ⁢                                                            ∂                  2                                ⁢                w                                            ∂                                  z                  2                                                                    =        0.                            (        11        )            
To construct a piezoelectric transformer, a known method is to combine the 31 and 33 mode piezoelectric systems of FIGS. 1 and 3. In such a piezoelectric transformer, a Rosen-type piezoelectric transformer for example, the side electrodes can be used as the input terminals and the end electrodes as the output terminals. Note the same terminology of the side and end electrodes as that used in the above description of the systems of FIGS. 1 and 3. The side and end electrodes are those plated on the largest and smallest surfaces of the elongated thin-plate workpiece respectively.
Traditional circuit analysis for a Rosen-type piezoelectric transformer may be developed based on the equivalent circuits of FIGS. 2 and 4 as both are combined to construct the transformer. For example, for a Rosen-type piezoelectric transformer put to operate on its second resonant frequency, an equivalent circuit can be derived as shown in FIG. 5. However, the equivalent circuit of FIG. 5 is derived by employing a considerable level of simplifications in the process of its theoretical development. These mathematical simplifications based on physically reasonable assumptions are necessary in order to avoid a mathematical system that may become excessively complex to analyze and to seek solution.
Though, this traditional approach has at least a few drawbacks. As the mechanical parameters of a piezoelectric workpiece are incorporated into the equivalent circuit for analysis based purely on circuit theories, some critical mechanical parameters diminish or even disappear in the process. These lost characteristics of a piezoelectric system that should otherwise have been preserved in the mathematical model of the system imply less flexible or even lost design parameters. Those characteristics, if preserved, may lead to the construction of better piezoelectric systems.
For example, the system performance characteristics such as energy conversion efficiency can not be optimized. This is due to the fact that circuits interfacing with the piezoelectric workpiece including both the driving circuit and the load have to be designed by considering the circuit configuration based on the equivalent circuit of the piezoelectric workpiece. However, the equivalent circuit is not the best model of the piezoelectric body as its mechanical characteristics are not fully encompassed in circuit theory-based models.
The result obtained from the conventional circuit theory in the analysis of a piezoelectric transducer system thus is not the best possible result. This is a fact reflected by the harmonics existing in the output of a piezoelectric system constructed in accordance with the developed result. The presence of these harmonics reduces overall system efficiency, and also incurs other problems such as load matching due to the existence of the undesirable harmonics.
Accordingly, it is an object of the present invention to provide a piezoelectric transducer apparatus having a modal-shaped electrode that operates in a resonant mode without significant undesirable harmonics of non-resonant frequencies.
It is another object of the present invention to provide a piezoelectric transducer apparatus having a modal-shaped electrode that achieves high operating efficiency in converting energy.
It is a further object of the present invention to provide a piezoelectric transformer having a modal-shaped electrode that outputs an AC electric power without significant undesirable harmonics.
These and other objects are achieved in an innovative piezoelectric transducer apparatus having a piezoelectric workpiece with a modal-shaped actuator electrode for converting an input energy of one form into an output energy of another form. The piezoelectric workpiece comprises an actuator section and a sensor section. The actuator section is formed in the piezoelectric workpiece and has a modal-shaped electrode for exciting the piezoelectric workpiece into mechanical vibration upon driven by the input energy. The sensor section is also formed in the piezoelectric workpiece and has a sensor electrode for delivering the output energy to an external load of the apparatus by picking up the energy generated by the excitation. The modal-shaped actuator electrode has a shape function defined by the mathematical solution function of the governing equation of the piezoelectric workpiece under the condition that the piezoelectric workpiece being vibrating in a selected resonant mode.